Question: Solve for $x$ and $y$ using elimination. ${2x+y = 19}$ ${5x-y = 23}$
We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $y$ and $-y$ cancel out. $7x = 42$ $\dfrac{7x}{{7}} = \dfrac{42}{{7}}$ ${x = 6}$ Now that you know ${x = 6}$ , plug it back into $\thinspace {2x+y = 19}\thinspace$ to find $y$ ${2}{(6)}{ + y = 19}$ $12+y = 19$ $12{-12} + y = 19{-12}$ ${y = 7}$ You can also plug ${x = 6}$ into $\thinspace {5x-y = 23}\thinspace$ and get the same answer for $y$ : ${5}{(6)}{ - y = 23}$ ${y = 7}$